Value-sharing and uniqueness problems for non-Archimedean differential polynomials in several variables

Abstract

We consider differential polynomials of Fermat–Waring type, const-ructed using polynomials of Yi’s type for meromorphic functions in a non-Archimedean field. Similarly to the Hayman Conjecture, we prove that the considered differential polynomials assume all values. We established also a uniqueness theorem for these differential polynomials.